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I understand that with simple linear regression, each estimated coefficient has an associated p-value that corresponds to the null hypothesis that the coefficient in question is 0. If this p-value is less than some significance level, then we reject that null hypothesis.

Does the same thing hold for results coming from a VAR model used to fit multivariate time series data? For example, I'm looking at this output from statsmodels:

Results for equation Y
=============================================================================================================
            coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------
const       -137462.630878   2366245.152723       -0.058            0.954
L1.Y        -0.627474         0.063546            -9.874            0.000
L1.X        -708.839187      2858.506570          -0.248            0.804
=============================================================================================================

How do I interpret those prob values? Is the hypothesis the same as for linear regression, in which case the hypothesis that the L1.X coefficient is 0 cannot be rejected? Furthermore, where can I learn more about how these probabilities are calculated? In my experience, most linear regression texts emphasis the hypothesis testing quite a bit, but I don't see any such sections when I look in time series books. What am I missing?

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  • $\begingroup$ Depending on the structure of the model and actual approach used, VAR models can be fitted using OLS, which would provide the same p-values with the same interpretation as you are used to (not necessarily correct). If FGLS is used, the std. errors should be adjusted appropriately. Some slides here. See Lütkepohl for when FGLS is needed for VAR and when OLS is can work too. $\endgroup$ – runr Jul 30 '20 at 1:40

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